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Expression of type Equals

from the theory of proveit.physics.quantum.QPE

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, Variable, k
from proveit.core_expr_types import Len
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, i, one, pi, two
from proveit.physics.quantum import NumKet
from proveit.physics.quantum.QFT import InverseFourierTransform
from proveit.physics.quantum.QPE import _m_domain, _phase, _t
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Equals(Len(operands = [InverseFourierTransform(_t), VecSum(index_or_indices = [k], summand = ScalarMult(Exp(e, Mult(two, pi, i, _phase, k)), NumKet(k, _t)), domain = _m_domain)]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, two)]))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
|\left({\mathrm {FT}}^{\dag}_{t}, \sum_{k=0}^{2^{t} - 1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot k} \cdot \lvert k \rangle_{t}\right)\right)| = |\left(1, \ldots, 2\right)|
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operands: 5
4Operationoperator: 6
operands: 7
5ExprTuple8, 9
6Literal
7ExprTuple10
8Operationoperator: 11
operand: 54
9Operationoperator: 13
operand: 16
10ExprRangelambda_map: 15
start_index: 55
end_index: 53
11Literal
12ExprTuple54
13Literal
14ExprTuple16
15Lambdaparameter: 20
body: 20
16Lambdaparameter: 46
body: 19
17ExprTuple20
18ExprTuple46
19Conditionalvalue: 21
condition: 22
20Variable
21Operationoperator: 23
operands: 24
22Operationoperator: 25
operands: 26
23Literal
24ExprTuple27, 28
25Literal
26ExprTuple46, 29
27Operationoperator: 49
operands: 30
28Operationoperator: 31
operands: 32
29Operationoperator: 33
operands: 34
30ExprTuple35, 36
31Literal
32ExprTuple46, 54
33Literal
34ExprTuple37, 38
35Literal
36Operationoperator: 39
operands: 40
37Literal
38Operationoperator: 41
operands: 42
39Literal
40ExprTuple53, 43, 44, 45, 46
41Literal
42ExprTuple47, 48
43Literal
44Literal
45Literal
46Variable
47Operationoperator: 49
operands: 50
48Operationoperator: 51
operand: 55
49Literal
50ExprTuple53, 54
51Literal
52ExprTuple55
53Literal
54Literal
55Literal